Advertisement

Reliable Computing

, Volume 5, Issue 1, pp 3–12 | Cite as

Efficient Control of the Dependency Problem Based on Taylor Model Methods

  • Kyoko Makino
  • Martin Berz
Article

Abstract

It is shown how the Taylor Model approach allows the rigorous description of functional dependencies with far-reaching control of the dependency problem. The amount of overestimation decreases with a high power of the interval over which the information is required, at a computational expense that increases rather moderately with the dimensionality of the problem. This leads to the possibility of treating even cases with a very significant dependency problem that are intractable using conventional methods.

Keywords

Mathematical Modeling High Power Conventional Method Computational Mathematic Industrial Mathematic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berz, M.: Computational Differentiation, Entry in: Encyclopedia of Computer Science and Technology, Marcel Dekker, New York, in preparation.Google Scholar
  2. 2.
    Berz, M.: Differential Algebraic Techniques, Entry in: Tigner, M. and Chao, A. (eds), Handbook of Accelerator Physics and Engineering, World Scientific, New York, in print.Google Scholar
  3. 3.
    Berz, M.: Forward Algorithms for High Orders and Many Variables, Automatic Differentiation of Algorithms: Theory, Implementation and Application, SIAM, 1991.Google Scholar
  4. 4.
    Berz, M.: Higher Order Derivatives and Taylor Models, Entry in: Encyclopedia of Optimization, Kluwer Academic Publisher, Boston, 1997.Google Scholar
  5. 5.
    Berz, M.: High-Order Computation and Normal Form Analysis of Repetitive Systems, in: Month, M. (ed.), Physics of Particle Accelerators, AIP 249, American Institute of Physics, 1991, p. 456.Google Scholar
  6. 6.
    Berz, M., Bischof, C., Corliss, G., and Griewank, A. (eds): Computational Differentiation: Techniques, Applications, and Tools, SIAM, Philadelphia, 1996.Google Scholar
  7. 7.
    Berz, M. and Hoffstätter, G.: Computation and Application of Taylor Polynomials with Interval Remainder Range Enclosure, Reliable Computing 4(1) (1998), pp. 83-97.Google Scholar
  8. 8.
    Berz, M., Makino K., Shamseddine, K., and Wan, W.: Applications of Modern Map Methods in Particle Beam Physics, Academic Press, Orlando, Florida, 1998, in print.Google Scholar
  9. 9.
    Griewank, A., Corliss, G. F., and Eds.: Automatic Differentiation of Algorithms, SIAM, Philadelphia, 1991.Google Scholar
  10. 10.
    Makino, K. and Berz, M.: Remainder Differential Algebras and Their Applications, in: Berz, M., Bischof, C., Corliss, G., and Griewank, A. (eds.), Computational Differentiation: Techniques, Applications, and Tools, SIAM, 1996, pp 63-74.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Kyoko Makino
    • 1
  • Martin Berz
    • 1
  1. 1.Department of Physics and Astronomy and National Superconducting Cyclotron LaboratoryMichigan State UniversityEast LansingUSA

Personalised recommendations